Gini coefficient would be interesting, but irrelevant for BM.
It requires a large sample so that the "top portion" is a meaningful group as is the "bottom portion." Assuming a realm of 30 nobles, comparing the top 10% to the bottom 10% is comparing 3 dukes to 3 new knights with no oaths. Comparing 2 samples of 3 is not very useful.
It could be interesting if set on a distribution of sorts with categorical labels, so that "comparatively equal" realms would get more.
But, better measures would be:
Average or median ratio of a lord's income to his/her knight's income (I think this would be an excellent measure, as it basically shows the oath shares being offered)
Ratio of gold given manually vs. through oaths (as Tim suggested)
A "haves and have-nots" Gini coefficient, wherein the income of the top 50% is compared to the bottom 50%
Economics is my course of study. If I think about this for a while, I can find us probably at least a dozen reasonable measures of inequality. And a way to weight and aggregate them. I might even color-code it. You have no idea how fun that would be for me. Give... me.... data!
